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FREE-VIBRATION ANALYSIS OF THIN RECTANGULAR FLAT PLATES USING ORDINARY FINITE DIFFERENCE METHOD

Keywords: Boundary Conditions , Characteristic Equation , Eigen values and Eigenvectors , Fundamental Natural Frequency , Ordinary Finite Difference Method , Resonance.

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Abstract:

Earlier solutions on pure bending of thin rectangular flat plates were based on the use of trigonometrical series. However, series method has the problem of improper representation of deformed shape of plate in vibration. For such problems, the use of numerical methods for approximate solutions becomes necessary. In this study, Ordinary Finite Difference method (OFDM) as one of the popular numericaltechniques was used in free vibration (FB) analysis of thin rectangular flat plate. The differential equations of the biharmonic plate were transformed to fit the chosen grid pattern and these transformed equations were expressed in finite difference (FD)form. These differences were evaluated at each nodal point to obtain a set of simultaneous algebraic equations that were solved for the unknown functional values after using the proper boundary conditions of SSSS, CCCC and CSCS respectively. Visual Basic (VB) software program was developed and used in solving the algebraic equations, while the resulting natural frequencies , were compared with the exactvalues for an aspect ratio of 1.0 as shown in tables 1, 2 and 3 respectively. The solutions obtained in this study approximated closely to the exact solutions as shown in the tables. Hence, ordinary finite difference method (OFDM) provides simple and approximate solutions that are very close to exact values for this family of problems.

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